Magnetic Force on a Charged Particle Magnetic Force
![-Magnetic Force on a Charged Particle -Magnetic Force on a Current-Carrying Wire -Torque on -Magnetic Force on a Charged Particle -Magnetic Force on a Current-Carrying Wire -Torque on](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-1.jpg)
![• A magnetic field can exert a force on a charged particle that • A magnetic field can exert a force on a charged particle that](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-2.jpg)
![Three ways we talk about “magnetic field”. • Magnetic Field: Regions surrounding a magnet Three ways we talk about “magnetic field”. • Magnetic Field: Regions surrounding a magnet](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-3.jpg)
![Poles • Law of Poles: Like poles repel, unlike poles attract. • The force Poles • Law of Poles: Like poles repel, unlike poles attract. • The force](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-4.jpg)
![Force on a Charged Particle Moving in a Magnetic Field -Magnetic fields only exert Force on a Charged Particle Moving in a Magnetic Field -Magnetic fields only exert](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-5.jpg)
![Remember: Cross Product Using Determinants or Remember: Cross Product Using Determinants or](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-6.jpg)
![Remember: Properties of Cross Products of Unit Vectors ixi=0 jxj=0 kxk=0 ixj=k jxk=i kxi=j Remember: Properties of Cross Products of Unit Vectors ixi=0 jxj=0 kxk=0 ixj=k jxk=i kxi=j](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-7.jpg)
![To find the direction of the force use the Right Hand Rule For a To find the direction of the force use the Right Hand Rule For a](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-8.jpg)
![For a negative particle the F is opposite to what it would be for For a negative particle the F is opposite to what it would be for](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-9.jpg)
![Alternate Rule: Right Hand Curl Rule • Curl fingers from v to B F Alternate Rule: Right Hand Curl Rule • Curl fingers from v to B F](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-10.jpg)
![Graphical Representation of the Magnetic Field Vector (Strength), B x field lines pointing into Graphical Representation of the Magnetic Field Vector (Strength), B x field lines pointing into](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-11.jpg)
![Question • Find the direction of the magnetic force acting on the +charged particle Question • Find the direction of the magnetic force acting on the +charged particle](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-12.jpg)
![What motion will the particle in the previous example undergo (particle entered the Bfield What motion will the particle in the previous example undergo (particle entered the Bfield](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-13.jpg)
![Examples: http: //physicslearning. colorado. edu/Pira. Home/Physics. Drawings. htm Examples: http: //physicslearning. colorado. edu/Pira. Home/Physics. Drawings. htm](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-14.jpg)
![Does the magnetic force do work? • F is always perpendicular to the displacement Does the magnetic force do work? • F is always perpendicular to the displacement](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-15.jpg)
![Mass Spectrometer U. S. Department of Energy http: //doegenomestolife. org Mass Spectrometer U. S. Department of Energy http: //doegenomestolife. org](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-16.jpg)
![Motion of Alpha- Beta-Gamma Particles in a Magnetic Field 1) Alpha particles, positive helium Motion of Alpha- Beta-Gamma Particles in a Magnetic Field 1) Alpha particles, positive helium](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-17.jpg)
![Problem 1 A proton is accelerated through a constant electric field (parallel plates) and Problem 1 A proton is accelerated through a constant electric field (parallel plates) and](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-18.jpg)
![Problem 1 cont’d b) Calculate the force acting on the charge due to the Problem 1 cont’d b) Calculate the force acting on the charge due to the](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-19.jpg)
![Problem 1 cont’d c) Calculate the distance on the detector where the particle will Problem 1 cont’d c) Calculate the distance on the detector where the particle will](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-20.jpg)
![Large Hadron Collider CERN (Conseil Européen pour la Recherche Nucléaire) Switzerland- France 2008 Circumference: Large Hadron Collider CERN (Conseil Européen pour la Recherche Nucléaire) Switzerland- France 2008 Circumference:](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-21.jpg)
![• Particle Accelerators use electric and magnetic fields to accelerate charged particles. • • Particle Accelerators use electric and magnetic fields to accelerate charged particles. •](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-22.jpg)
![Magnetic Force on a Current Carrying Wire F = I (L x B) = Magnetic Force on a Current Carrying Wire F = I (L x B) =](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-23.jpg)
![The force acting on a wire of arbitrary shape is the same as if The force acting on a wire of arbitrary shape is the same as if](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-24.jpg)
![What is the net force acting on this current-carrying loop? What is the net force acting on this current-carrying loop?](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-25.jpg)
![Which way will a loop turn? Which way will a loop turn?](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-26.jpg)
![Forces on a Current-Carrying Loop For B as shown: F 1 = F 3 Forces on a Current-Carrying Loop For B as shown: F 1 = F 3](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-27.jpg)
![Torque Acting on the Current-Carrying Loop F 2 = F 4 = Ia. B Torque Acting on the Current-Carrying Loop F 2 = F 4 = Ia. B](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-28.jpg)
![Torque Acting on the Current. Carrying Loop Torque Acting on the Current. Carrying Loop](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-29.jpg)
![Magnetic Force on a Current Carrying Wire • Lorentz Force- Magnetic Force on a Magnetic Force on a Current Carrying Wire • Lorentz Force- Magnetic Force on a](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-30.jpg)
![DC Motor DC Motor](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-31.jpg)
![DC Motor DC Motor](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-32.jpg)
![Problem #9 A proton moves with a velocity of v=(2 i-4 j+k)m/s in a Problem #9 A proton moves with a velocity of v=(2 i-4 j+k)m/s in a](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-33.jpg)
![Problem #13 A wire 2. 80 m in length carries a current of 5. Problem #13 A wire 2. 80 m in length carries a current of 5.](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-34.jpg)
![Problem # 21 A small bar magnet is suspended in a uniform 0. 250 Problem # 21 A small bar magnet is suspended in a uniform 0. 250](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-35.jpg)
![Problem #54 A 0. 200 -kg metal rod carrying a current of 10. 0 Problem #54 A 0. 200 -kg metal rod carrying a current of 10. 0](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-36.jpg)
- Slides: 36
![Magnetic Force on a Charged Particle Magnetic Force on a CurrentCarrying Wire Torque on -Magnetic Force on a Charged Particle -Magnetic Force on a Current-Carrying Wire -Torque on](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-1.jpg)
-Magnetic Force on a Charged Particle -Magnetic Force on a Current-Carrying Wire -Torque on a Current-Carrying Loop Fermi Lab, Chicago Illinois Circumference 6. 3 km Mass Spectrometer DC Motor AP Physics C Mrs. Coyle
![A magnetic field can exert a force on a charged particle that • A magnetic field can exert a force on a charged particle that](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-2.jpg)
• A magnetic field can exert a force on a charged particle that moves in it.
![Three ways we talk about magnetic field Magnetic Field Regions surrounding a magnet Three ways we talk about “magnetic field”. • Magnetic Field: Regions surrounding a magnet](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-3.jpg)
Three ways we talk about “magnetic field”. • Magnetic Field: Regions surrounding a magnet where another magnet or a moving electric charge will feel a force of attraction or repulsion. • Magnetic Field Lines: exit the north pole and enter the south. • Magnetic Field Strength, B • Vector, Unit: Tesla, T • Named after Nikola Tesla
![Poles Law of Poles Like poles repel unlike poles attract The force Poles • Law of Poles: Like poles repel, unlike poles attract. • The force](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-4.jpg)
Poles • Law of Poles: Like poles repel, unlike poles attract. • The force between two poles varies as the inverse square of the distance between them. • A single pole (monopole) has not been isolated.
![Force on a Charged Particle Moving in a Magnetic Field Magnetic fields only exert Force on a Charged Particle Moving in a Magnetic Field -Magnetic fields only exert](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-5.jpg)
Force on a Charged Particle Moving in a Magnetic Field -Magnetic fields only exert forces on moving charged particles or other magnets. • F = |q|(v x B) = |q|v. B sin q • vector cross-product • q is the angle between v and B • F=0 for q =0 or 1800
![Remember Cross Product Using Determinants or Remember: Cross Product Using Determinants or](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-6.jpg)
Remember: Cross Product Using Determinants or
![Remember Properties of Cross Products of Unit Vectors ixi0 jxj0 kxk0 ixjk jxki kxij Remember: Properties of Cross Products of Unit Vectors ixi=0 jxj=0 kxk=0 ixj=k jxk=i kxi=j](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-7.jpg)
Remember: Properties of Cross Products of Unit Vectors ixi=0 jxj=0 kxk=0 ixj=k jxk=i kxi=j
![To find the direction of the force use the Right Hand Rule For a To find the direction of the force use the Right Hand Rule For a](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-8.jpg)
To find the direction of the force use the Right Hand Rule For a positive test charge: Thumb v Fingers B Out of palm F The force is always perpendicular to the v. B plane
![For a negative particle the F is opposite to what it would be for For a negative particle the F is opposite to what it would be for](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-9.jpg)
For a negative particle the F is opposite to what it would be for a positive particle (use left hand)
![Alternate Rule Right Hand Curl Rule Curl fingers from v to B F Alternate Rule: Right Hand Curl Rule • Curl fingers from v to B F](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-10.jpg)
Alternate Rule: Right Hand Curl Rule • Curl fingers from v to B F = q(v x B) • F is in the direction of the thumb • Similarly used for the direction of torque (t=r x F)
![Graphical Representation of the Magnetic Field Vector Strength B x field lines pointing into Graphical Representation of the Magnetic Field Vector (Strength), B x field lines pointing into](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-11.jpg)
Graphical Representation of the Magnetic Field Vector (Strength), B x field lines pointing into the page ● field lines pointing out of the page
![Question Find the direction of the magnetic force acting on the charged particle Question • Find the direction of the magnetic force acting on the +charged particle](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-12.jpg)
Question • Find the direction of the magnetic force acting on the +charged particle entering the magnetic field with a velocity v perpendicular to B. x x V x x x Answer: Upwards x x x
![What motion will the particle in the previous example undergo particle entered the Bfield What motion will the particle in the previous example undergo (particle entered the Bfield](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-13.jpg)
What motion will the particle in the previous example undergo (particle entered the Bfield in a direction perpendicular to B? • Circular Motion • Magnetic force will represent the centripetal force • http: //online. cctt. org/physicslab/content/ap plets/Java. Phys. Math/java/partmagn/index. html
![Examples http physicslearning colorado eduPira HomePhysics Drawings htm Examples: http: //physicslearning. colorado. edu/Pira. Home/Physics. Drawings. htm](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-14.jpg)
Examples: http: //physicslearning. colorado. edu/Pira. Home/Physics. Drawings. htm
![Does the magnetic force do work F is always perpendicular to the displacement Does the magnetic force do work? • F is always perpendicular to the displacement](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-15.jpg)
Does the magnetic force do work? • F is always perpendicular to the displacement • F can change the direction of v not the magnitude • F cannot do work, cannot change KE
![Mass Spectrometer U S Department of Energy http doegenomestolife org Mass Spectrometer U. S. Department of Energy http: //doegenomestolife. org](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-16.jpg)
Mass Spectrometer U. S. Department of Energy http: //doegenomestolife. org
![Motion of Alpha BetaGamma Particles in a Magnetic Field 1 Alpha particles positive helium Motion of Alpha- Beta-Gamma Particles in a Magnetic Field 1) Alpha particles, positive helium](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-17.jpg)
Motion of Alpha- Beta-Gamma Particles in a Magnetic Field 1) Alpha particles, positive helium nuclei, charge +2 e 2) Gamma rays, (no charge) electromagnetic radiation 3) Beta particles, electrons charge -1 e
![Problem 1 A proton is accelerated through a constant electric field parallel plates and Problem 1 A proton is accelerated through a constant electric field (parallel plates) and](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-18.jpg)
Problem 1 A proton is accelerated through a constant electric field (parallel plates) and acquires kinetic energy of 4 e. V. It enters perpendicularly to the 2 T field of a detector as shown. Charge of a proton=1. 6 x 10 -19 C, mass of proton=1. 67 x 10 -27 kg, ignore gravity. a) Draw the path of the positive charge as it enters the magnetic field.
![Problem 1 contd b Calculate the force acting on the charge due to the Problem 1 cont’d b) Calculate the force acting on the charge due to the](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-19.jpg)
Problem 1 cont’d b) Calculate the force acting on the charge due to the magnetic field. Charge of a proton=1. 6 x 10 -19 C , mass of proton=1. 67 x 10 -27 kg KE= 4 e. V B= 2 T Ans: v= 2. 77 x 104 m/s, F= 8. 86 x 10 -15 N
![Problem 1 contd c Calculate the distance on the detector where the particle will Problem 1 cont’d c) Calculate the distance on the detector where the particle will](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-20.jpg)
Problem 1 cont’d c) Calculate the distance on the detector where the particle will land (radius of the circular path). Ignore gravity. Charge of a proton=1. 6 x 10 -19 C, mass of proton=1. 67 x 10 -27 kg KE= 4 e. V B= 2 T Ans: 1. 45 x 10 -4 m
![Large Hadron Collider CERN Conseil Européen pour la Recherche Nucléaire Switzerland France 2008 Circumference Large Hadron Collider CERN (Conseil Européen pour la Recherche Nucléaire) Switzerland- France 2008 Circumference:](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-21.jpg)
Large Hadron Collider CERN (Conseil Européen pour la Recherche Nucléaire) Switzerland- France 2008 Circumference: 27 km
![Particle Accelerators use electric and magnetic fields to accelerate charged particles • Particle Accelerators use electric and magnetic fields to accelerate charged particles. •](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-22.jpg)
• Particle Accelerators use electric and magnetic fields to accelerate charged particles. • Cyclotron Applet
![Magnetic Force on a Current Carrying Wire F I L x B Magnetic Force on a Current Carrying Wire F = I (L x B) =](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-23.jpg)
Magnetic Force on a Current Carrying Wire F = I (L x B) = I L B sinq • I is the current • L is a vector of magnitude of the length of the wire and direction that of the current • q is the angle formed between I and B What is the direction of the magnetic force acting on this wire? F
![The force acting on a wire of arbitrary shape is the same as if The force acting on a wire of arbitrary shape is the same as if](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-24.jpg)
The force acting on a wire of arbitrary shape is the same as if it were a straight wire with the same ends • The total force is:
![What is the net force acting on this currentcarrying loop What is the net force acting on this current-carrying loop?](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-25.jpg)
What is the net force acting on this current-carrying loop?
![Which way will a loop turn Which way will a loop turn?](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-26.jpg)
Which way will a loop turn?
![Forces on a CurrentCarrying Loop For B as shown F 1 F 3 Forces on a Current-Carrying Loop For B as shown: F 1 = F 3](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-27.jpg)
Forces on a Current-Carrying Loop For B as shown: F 1 = F 3 = 0 F 2 = F 4 = Ia. B
![Torque Acting on the CurrentCarrying Loop F 2 F 4 Ia B Torque Acting on the Current-Carrying Loop F 2 = F 4 = Ia. B](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-28.jpg)
Torque Acting on the Current-Carrying Loop F 2 = F 4 = Ia. B Torque acting on the loop: Top View
![Torque Acting on the Current Carrying Loop Torque Acting on the Current. Carrying Loop](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-29.jpg)
Torque Acting on the Current. Carrying Loop
![Magnetic Force on a Current Carrying Wire Lorentz Force Magnetic Force on a Magnetic Force on a Current Carrying Wire • Lorentz Force- Magnetic Force on a](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-30.jpg)
Magnetic Force on a Current Carrying Wire • Lorentz Force- Magnetic Force on a Current Carrying Wire (Fendt Applet)
![DC Motor DC Motor](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-31.jpg)
DC Motor
![DC Motor DC Motor](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-32.jpg)
DC Motor
![Problem 9 A proton moves with a velocity of v2 i4 jkms in a Problem #9 A proton moves with a velocity of v=(2 i-4 j+k)m/s in a](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-33.jpg)
Problem #9 A proton moves with a velocity of v=(2 i-4 j+k)m/s in a region in which the magnetic field is B=(i+2 j-3 k)T. What is the magnitude of the magnetic force this charge experiences? Ans: 2. 34 x 10 -18 N
![Problem 13 A wire 2 80 m in length carries a current of 5 Problem #13 A wire 2. 80 m in length carries a current of 5.](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-34.jpg)
Problem #13 A wire 2. 80 m in length carries a current of 5. 00 A in a region where a uniform magnetic field has a magnitude of 0. 390 T. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is (a) 60. 0°, (b) 90. 0°, (c) 120°. Ans: a)4. 73 N, b)5. 46 N, c)4. 73 N
![Problem 21 A small bar magnet is suspended in a uniform 0 250 Problem # 21 A small bar magnet is suspended in a uniform 0. 250](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-35.jpg)
Problem # 21 A small bar magnet is suspended in a uniform 0. 250 -T magnetic field. The maximum torque experienced by the bar magnet is 4. 60 × 10– 3 N · m. Calculate the magnetic moment of the bar magnet. Ans: 18. 4 m. A m 2
![Problem 54 A 0 200 kg metal rod carrying a current of 10 0 Problem #54 A 0. 200 -kg metal rod carrying a current of 10. 0](https://slidetodoc.com/presentation_image/41c3a0193cd731c61397a4d4a20efca2/image-36.jpg)
Problem #54 A 0. 200 -kg metal rod carrying a current of 10. 0 A glides on two horizontal rails 0. 500 m apart. What vertical magnetic field is required to keep the rod moving at a constant speed if the coefficient of kinetic friction between the rod and rails is 0. 100? Ans: F=0. 196 N, B=0. 039 T
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